void
MAST::StructuralElementBase::transform_to_global_system(const libMesh::DenseMatrix<ValType>& local_mat,
libMesh::DenseMatrix<ValType>& global_mat) const {
libmesh_assert_equal_to( local_mat.m(), local_mat.n());
libmesh_assert_equal_to(global_mat.m(), global_mat.n());
libmesh_assert_equal_to( local_mat.m(), global_mat.m());
const unsigned int n_dofs = _fe->n_shape_functions();
global_mat.zero();
libMesh::DenseMatrix<ValType> mat;
mat.resize(6*n_dofs, 6*n_dofs);
const DenseRealMatrix& Tmat = _transformation_matrix();
// now initialize the global T matrix
for (unsigned int i=0; i<n_dofs; i++)
for (unsigned int j=0; j<3; j++)
for (unsigned int k=0; k<3; k++) {
mat(j*n_dofs+i, k*n_dofs+i) = Tmat(j,k); // for u,v,w
mat((j+3)*n_dofs+i, (k+3)*n_dofs+i) = Tmat(j,k); // for tx,ty,tz
}
// right multiply with T^T, and left multiply with T.
global_mat = local_mat;
global_mat.right_multiply_transpose(mat);
global_mat.left_multiply(mat);
}
void
MAST::StructuralElementBase::transform_to_local_system(const libMesh::DenseVector<ValType>& global_vec,
libMesh::DenseVector<ValType>& local_vec) const {
libmesh_assert_equal_to( local_vec.size(), global_vec.size());
const unsigned int n_dofs = _fe->n_shape_functions();
local_vec.zero();
DenseRealMatrix mat;
mat.resize(6*n_dofs, 6*n_dofs);
const DenseRealMatrix& Tmat = _transformation_matrix();
// now initialize the global T matrix
for (unsigned int i=0; i<n_dofs; i++)
for (unsigned int j=0; j<3; j++)
for (unsigned int k=0; k<3; k++) {
mat(j*n_dofs+i, k*n_dofs+i) = Tmat(j,k); // for u,v,w
mat((j+3)*n_dofs+i, (k+3)*n_dofs+i) = Tmat(j,k); // for tx,ty,tz
}
// left multiply with T^T
mat.vector_mult_transpose(local_vec, global_vec);
}
//bradius: bead size
//gap: distance between two rigid body;
//spacing: distance between two beads;
//N : The number of the beads on each body
int main(){
int N, nc = 4,i,j;
double bradius = 1.0; //1.0/(2*sqrt(2)),
double gap = 20.0, spacing=0.0;
double beta = 0.0;
int accuracy = 12, s = 80;
int size =pow(nc,3)+3*nc*pow(nc-1,2);
size = size *6;
double *ShellSphs, ShellRadius;
ShellSphs = (double*)calloc(size, sizeof(double));
/*===============================================================================
Step 1 : Construct the Shell representation
==============================================================================*/
//Construct sphere 1
N = shell_model(nc, bradius,spacing, &ShellRadius, ShellSphs);
double length = 2*ShellRadius;
printf("Sphs1, N=%d,ShellRadius = %f\n", N, ShellRadius);
//for (i=0;i<N; i++)
// printf("%.2f, %.2f, %.2f\n", ShellSphs[3*i], ShellSphs[3*i+1], ShellSphs[3*i+2]);
// Construct Sphere 2 from sphere 1
double offset = (2*ShellRadius + gap); // Distance between two sphere
printf("offset = %f\n", offset);
for(i=0; i< N; i++){
ShellSphs[3*(N+i)] = ShellSphs[3*i];
ShellSphs[3*(N+i)+1] = ShellSphs[3*i+1];
ShellSphs[3*(N+i)+2] = ShellSphs[3*i+2]+ offset;
}
printf("Sphs2 is \n");
for(i=N;i<2*N; i++)
printf("%.2f, %.2f, %.2f\n", ShellSphs[3*i], ShellSphs[3*i+1], ShellSphs[3*i+2]);
// Matrix computation
double *T1;
T1 = (double*)calloc(3*N*6, sizeof(double)); //3N*6
//Compute T matrix
Tmat(T1, ShellSphs, N);
/*================================================================================
Step 2 : Given the external body Force, compute the body velocity
Assume A = T'*D^{-1}*T,
T = ( T1
T2 )
compute AV = F
Note : Here, since the two sphere are with the same no. of beads,T1 = T2 = T.
================================================================================*/
double *F0, *V0, *F,*V;
F0 = (double *)calloc(6*N+12, sizeof(double));
V0 = (double *)calloc(6*N+12, sizeof(double));
F = (double *)calloc(12, sizeof(double));
V = (double *)calloc(12, sizeof(double));
for (i=0; i<6*N+12; i++){
F0[i]=0.0;
}
F[2] = 1.0;
F0[6*N+2] = 1.0;
GMRES_FMM(bradius, length, beta, s, accuracy, 2*N, ShellSphs, T1, F0, V0);
BCG_FMM(bradius, length, beta, s, accuracy, 2*N, ShellSphs, T1, F, V);
for (i=0;i<12; i++){
printf("%f\n",V0[6*N+i]);
}
free(ShellSphs);
free(T1);
free(F0);
free(V0);
free(F);
free(V);
return 0;
}
